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"date": "2026-09-21", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_31 quotient logical", "seeds": [ 0 ] } }, "Z": { "value": 66, "confidence": "upper_bound", "witness": [ 16, 18, 24, 27, 47, 49, 55, 58, 78, 80, 86, 89, 109, 111, 117, 120, 140, 142, 148, 151, 171, 173, 179, 182, 202, 204, 210, 213, 233, 235, 241, 244, 264, 266, 272, 275, 295, 297, 303, 306, 326, 328, 334, 337, 343, 344, 374, 375, 405, 406, 436, 437, 467, 468, 498, 499, 529, 530, 560, 561, 591, 592, 622, 623, 653, 654 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-21", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_31 quotient logical", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@natestemen" ], "construction": "Generalized bicycle on Z_341 = Z_11 x Z_31 (n = 2*341): H_X = [A|B], H_Z = [B^T|A^T] with circulant A, B built from exponent supports a = [37, 55, 71, 102, 159, 169, 172, 182, 190, 244, 246, 265, 268, 272, 290, 301] (weight 16) and b = [0, 11, 70, 81, 114, 153, 217, 227, 228, 235, 268, 280, 311, 320, 323, 339] (weight 16); row i of a circulant has a 1 in column (i + e) mod 341 for each exponent e. Both supports are codewords of a designed divisor ideal of x^341 - 1, mined by masked randomized-information-set search with subgroup-quotient cleanliness filters; k = 2 deg gcd(a(x), b(x), x^341 - 1) = 182.", "origin": "submission", "date": "2026-08-28", "model": "Claude Fable 5", "notes": "Witness-backed upper bound, not an exact-distance claim. Screening ladder (randomized information-set trials -> lightest logical): 200000 -> d<=81, 2000000 -> d<=75, 20000000 -> d<=75. Both witnesses have weight 75: the family's block-swap plus index-reversal symmetry maps an X-logical to a Z-logical of equal weight, and both were revalidated independently against the verifier's criteria (in the correct kernel, outside the opposite stabilizer rowspace)." }, "family": "generalized-bicycle" }